The aim of studying and bibliography

The main aim of study: The aim of the course is to familiarize students with the basic concepts of mathematical analysis, such as multiple integral, line integral, surface integral and their applications and to familiarize with the theory of field..

The general information about the module: The module consists of 30 hours of lectures and 45 hours of exercises, ends with an exam.

Bibliography required to complete the module

Bibliography used during lectures

1	F. Leja	Rachunek różniczkowy i całkowy	PWN, Warszawa.	1976
2	G. M. Fichtenholz	Rachunek różniczkowy i całkowy	PWN, Warszawa.	2004
3	W. Rudin	Podstawy analizy matematycznej	PWN, Warszawa.	1982

Bibliography used during classes/laboratories/others

1	G.Berman	Zbiór zadań z analizy matematycznej	Pracownia Komputerowa Jacka Skalmierskiego, Gliwice.	2000
2	W.Stankiewicz, J.Wójtowicz	Zadania z matematyki dla wyższych uczelni technicznych cz.2	PWN, Warszawa.	1978

Bibliography to self-study

1	W.Krysicki, L.Włodarski	Analiza matematyczna w zadaniach cz.2	PWN, Warszawa.	2000
2	J.Stankiewicz, K.Wilczek	Rachunek różniczkowy i całkowy funkcji wielu zmiennych	Oficyna Wydawnicza PRz, Rzeszów.	2005

Basic requirements in category knowledge/skills/social competences

Formal requirements: The student satisfies the formal requirements set out in the study regulations

Basic requirements in category knowledge: Differential calculus of functions of several variables, partial derivatives, indefinite integrals.

Basic requirements in category skills: student can calculate limits of functions, indefinite and definite integrals

Basic requirements in category social competences: Ability of individual and group learning, awaresness of the level of own knowledge

Module outcomes

MEK	The student who completed the module	Types of classes / teaching methods leading to achieving a given outcome of teaching	Methods of verifying every mentioned outcome of teaching	Relationships with KEK	Relationships with PRK
01	Student can calculate simple double integrals and the triple integrals .	lectures, solving classes	test	K_W01+ K_W02+ K_W03+ K_W04+ K_W07+ K_U04+ K_U05++ K_U17+ K_K04+ K_K07+	P7S_KK P7S_KO P7S_KR P7S_UW P7S_WG P7S_WK
02	Student can calculate simple curve integrals of a scalar and vector field.	lectures, solving classes	test, written exam	K_W01+ K_W03+ K_W04+ K_W05+ K_U05++ K_U13+ K_K04+	P7S_KO P7S_KR P7S_UK P7S_UW P7S_WG
03	Student knows the basis of the field theory. He can calculate the potential of the field in simply examples.	lecture, solving classes	test	K_W01++ K_W02+ K_W03+ K_W05+ K_U03+ K_U04+ K_U05+ K_U14+ K_K04+	P7S_KO P7S_KR P7S_UW P7S_WG P7S_WK
04	student can calculate the surface integral in simply examples	lecture, solving classes	test, written exam	K_W01+ K_W03+ K_W05+ K_U01+ K_U02+ K_U05+ K_U08+ K_U15+ K_K01+ K_K02+ K_K04+	P7S_KK P7S_KO P7S_KR P7S_UK P7S_UO P7S_UU P7S_UW P7S_WG

Attention: Depending on the epidemic situation, verification of the achieved learning outcomes specified in the study program, in particular credits and examinations at the end of specific classes, can be implemented remotely (real-time meetings).

The syllabus of the module

Sem.	TK	The content	realized in	MEK
2	TK01	The concept of double integral. Changing of double integral onto iterative integrals. Triple integral. Changing of triple integral onto iterative integrals. Applications of multiple integrals.	W01 - W05, C01-C05	MEK01
2	TK02	Curve integral of a scalar field, its properties and applications. Curve integral of a vector field and methods of its evaluating. Green theorem and its applications.	W06 - W09, C06-C09	MEK01 MEK02
2	TK03	The basis of the theory of field: a gradient, a potential, a divergence, a curl and a circulation of the vector field.	W10 - W11, C10-C11	MEK02 MEK03
2	TK04	The concept of the surface integral of a scalar field and of a vector field. Properties of surface integrals. Applications of surface integral in the field theory. Gauss-Ostrogradski theorem and Stokes theorem. Differential forms.	W12 - W15, C12-C15	MEK01 MEK04

The student's effort

The type of classes	The work before classes	The participation in classes	The work after classes
Lecture (sem. 2)		contact hours: 30.00 hours/sem.	complementing/reading through notes: 5.00 hours/sem. Studying the recommended bibliography: 10.00 hours/sem.
Class (sem. 2)	The preparation for a Class: 10.00 hours/sem. The preparation for a test: 10.00 hours/sem.	contact hours: 45.00 hours/sem.	Finishing/Studying tasks: 15.00 hours/sem.
Advice (sem. 2)	The preparation for Advice: 5.00 hours/sem.	The participation in Advice: 5.00 hours/sem.
Exam (sem. 2)	The preparation for an Exam: 12.00 hours/sem.	The written exam: 3.00 hours/sem.

The way of giving the component module grades and the final grade

The type of classes	The way of giving the final grade
Lecture	Written or oral exam. Exam only after the credit of classes.
Class	Two written tests and activity during classes.
The final grade	The final grade is the average of grade of classes and grade of the exam.

Sample problems

Required during the exam/when receiving the credit
(-)

Realized during classes/laboratories/projects
(-)

Others
(-)

Can a student use any teaching aids during the exam/when receiving the credit : no

The contents of the module are associated with the research profile: yes

1	M. Nunokawa; J. Sokół; L. Trojnar-Spelina	Some results on p-valent functions	2023
2	R. Kargar; L. Trojnar-Spelina	Starlike functions associated with the generalized Koebe function	2021
3	M. Nunokawa; J. Sokół; L. Trojnar-Spelina	On a sufficient condition for function to be p-valent close-to-convex	2020
4	A. Ebadian; R. Kargar; L. Trojnar-Spelina	Further results for starlike functions related with Booth lemniscate	2019
5	L. Trojnar-Spelina; I. Włoch	On a new type of the companion Pell numbers	2019
6	L. Trojnar-Spelina; I. Włoch	On generalized Pell and Pell-Lucas numbers	2019
7	R. Kargar; L. Trojnar-Spelina	Some applications of differential subordination for certain starlike functions	2019